Caniza has always been a regular in the Paraguay national football team because of his versatility, as he can play as a side defender or as a centre-back. After the 2006 FIFA World Cup, Caniza announced his retirement from the Paraguay national team. However, when coach Gerardo Martino took the helm of the national team Caniza was called back and accepted to return to play for Paraguay. After Gerardo Martino took the head coach job in the Paraguay national football team, Caniza was voted for his teammates to become the captain of the team, so every time he plays (when he is not injured or suspended) he captains the Paraguay national football team.

Caniza holds the distinction as the only Paraguayan footballer to be selected for 4 consecutive FIFA World Cup Finals squads, having been chosen in 1998, 2002, 2006 and 2010.

Due to his small size and industrial play, he has been described by BBC South American reporter Tim Vickery as "the Paraguayan Nobby Stiles".